Covariance matrix for a d-dimensional gaussian

41 Views Asked by At

I am given that the second derivative of the log-likelihood to be $$ \frac{d^2\ell}{d\boldsymbol{\mu}^2} = -\Sigma^{-1}*n $$

$\Sigma$ is the covariance matrix and $n$ is the number of random variables. Why is this expression always negative? Is there some property of the covariance matrix that I am unaware of that makes the inverse of this matrix only have positive elements?